Fig. A.1

The difficulty of finding a proper center of mass. We consider three clumps p1, p2, p3 moving at velocities v1, v2, v3. If we are interested in whether i is gravitationally bound, since the majority of attraction comes from p1, physically the center of mass should be the center of mass of p1 instead of the center of mass of the three clumps p1, p2, p3, since p2 and p3 do not contribute much gravitational attraction to i compared to p1. Therefore to estimate the gravitational boundedness, a naive calculation of the center of mass where all the mass in the whole cloud is included is not appropriate. In the case of a complicated distribution of gas, finding the center of mass is not straightforward.
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